Noncanonical warm inflation: a model with a general Lagrangian density

Warm inflation is extended from the canonical field to the noncanonical field with a general Lagrangian density having coupling form of kinetic and potential terms. We develop the motion equation of the noncanonical inflaton field, and notice the motion equation has an annoying coupling term $\mathcal{L}_{X\varphi}\dot\varphi^2$, which makes the inflation difficult to solve. It is found that a special field redefinition exists, making the motion equation of inflaton uncoupled. Then we can solve inflation in the special field representation for convenience. The relation of field redefinition between the special uncoupled field and general noncanonical field is obtained. The motion equations and slow roll approximations of noncanonical warm inflation in the special field representation are developed. Then we give two examples to show how to translate a general noncanonical Lagrangian density in the coupled $\varphi$ representation, to the uncoupled $\phi$ representation. Finally, the cosmological perturbations generated by the new kind of warm inflation is calculated.